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The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of a
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
in relation to an observer who is moving relative to the wave source. It is named after the
Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
n physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a
vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), ...
sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession. The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wave fronts is reduced, so the waves "bunch together". Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves "spread out". For waves that propagate in a medium, such as
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as electromagnetic waves or
gravitational waves Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside i ...
, only the relative difference in velocity between the observer and the source needs to be considered. When this relative velocity is not negligible compared to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
, a more complicated relativistic Doppler effect arises.


History

Doppler first proposed this effect in 1842 in his treatise "'' Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels''" (On the coloured light of the
binary stars A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in w ...
and some other stars of the heavens).Alec Eden ''The search for Christian Doppler'', Springer-Verlag, Wien 1992. Contains a facsimile edition with an
English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ...
translation.
The hypothesis was tested for sound waves by
Buys Ballot Christophorus Henricus Diedericus Buys Ballot (; October 10, 1817 – February 3, 1890) was a Dutch chemist and meteorologist after whom Buys Ballot's law and the Buys Ballot table are named. He was first chairman of the International Meteo ...
in 1845. He confirmed that the sound's pitch was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
s in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal).Fizeau: "Acoustique et optique". ''Lecture, Société Philomathique de Paris'', 29 December 1848. According to Becker(pg. 109), this was never published, but recounted by M. Moigno(1850): "Répertoire d'optique moderne" (in French), vol 3. pp 1165–1203 and later in full by Fizeau, "Des effets du mouvement sur le ton des vibrations sonores et sur la longeur d'onde des rayons de lumière"; aris, 1870 ''Annales de Chimie et de Physique'', 19, 211–221. In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).


General

In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency f and emitted frequency f_\text is given by: f = \left( \frac \right) f_0 where *c is the propagation speed of waves in the medium; *v_\text is the speed of the receiver relative to the medium, added to c if the receiver is moving towards the source, subtracted if the receiver is moving away from the source; *v_\text is the speed of the source relative to the medium, added to c if the source is moving away from the receiver, subtracted if the source is moving towards the receiver. Note this relationship predicts that the frequency will decrease if either source or receiver is moving away from the other. Equivalently, under the assumption that the source is either directly approaching or receding from the observer: \frac = \frac = \frac where *v_ is the wave's velocity relative to the receiver; *v_ is the wave's velocity relative to the source; *\lambda is the wavelength. If the source approaches the observer at an angle (but still with a constant velocity), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a
monotonic In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order ...
decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual. If the speeds v_\text and v_\text \, are small compared to the speed of the wave, the relationship between observed frequency f and emitted frequency f_\text is approximately where *\Delta f = f - f_0 *\Delta v = -(v_\text - v_\text) is the opposite of the velocity of the receiver relative to the source: it is positive when the source and the receiver are moving towards each other. File:Dopplereffectstationary.gif, Stationary sound source produces sound waves at a constant frequency , and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where . File:Dopplereffectsourcemovingrightatmach0.7.gif, The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed . Since the source is moving, the centre of each new
wavefront In physics, the wavefront of a time-varying '' wave field'' is the set ( locus) of all points having the same '' phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal fr ...
is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency and an observer behind the source will hear a lower frequency . File:Dopplereffectsourcemovingrightatmach1.0.gif, Now the source is moving at the speed of sound in the medium (). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives and an observer behind the source will hear a lower frequency . File:Dopplereffectsourcemovingrightatmach1.4.gif, The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 ''c''. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect nothing and an observer behind the source will hear a lower frequency .


Consequences

With an observer stationary relative to the medium, if a moving source is emitting waves with an actual frequency f_0 (in this case, the wavelength is changed, the transmission velocity of the wave keeps constant; note that the ''transmission velocity'' of the wave does not depend on the ''velocity of the source''), then the observer detects waves with a frequency f given by f = \left ( \frac \right ) f_0 A similar analysis for a moving ''observer'' and a stationary source (in this case, the wavelength keeps constant, but due to the motion, the rate at which the observer receives waves and hence the ''transmission velocity'' of the wave
ith respect to the observer The Ith () is a ridge in Germany's Central Uplands which is up to 439 m high. It lies about 40 km southwest of Hanover and, at 22 kilometres, is the longest line of crags in North Germany. Geography Location The Ith is immediate ...
is changed) yields the observed frequency: f = \left ( \frac \right ) f_0 Assuming a stationary observer and a source moving at the speed of sound, the Doppler equation predicts a perceived momentary infinite frequency by an observer in front of a source that is traveling at the speed of sound. All the peaks are at the same place, so the wavelength is zero and the frequency is infinite. This overlay of all the waves produces a
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
which for sound waves is known as a sonic boom. When the source moves faster than the wave speed the source outruns the wave. The equation gives negative frequency values, which have no physical sense in this context (no sound at all will be heard by the observer until the source passes past them).
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. A ...
predicted the following effect in his classic book on sound: if the observer were moving from the (stationary) source at twice the speed of sound, a musical piece ''previously'' emitted by that source would be heard in correct tempo and pitch, but as if played ''backwards''.


Applications


Acoustic Doppler current profiler

An acoustic Doppler current profiler (ADCP) is a hydroacoustic current meter similar to a
sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances (ranging), communicate with or detect objects on o ...
, used to measure water current velocities over a depth range using the Doppler effect of sound waves scattered back from particles within the water column. The term ADCP is a generic term for all acoustic current profilers, although the abbreviation originates from an instrument series introduced by RD Instruments in the 1980s. The working frequencies range of ADCPs range from 38  kHz to several
Megahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one ...
. The device used in the air for wind speed profiling using sound is known as SODAR and works with the same underlying principles.


Robotics

Dynamic real-time path planning in robotics to aid the movement of robots in a sophisticated environment with moving obstacles often take help of Doppler effect. Such applications are specially used for competitive robotics where the environment is constantly changing, such as robosoccer.


Sirens

A
siren Siren or sirens may refer to: Common meanings * Siren (alarm), a loud acoustic alarm used to alert people to emergencies * Siren (mythology), an enchanting but dangerous monster in Greek mythology Places * Siren (town), Wisconsin * Siren, Wiscon ...
on a passing
emergency vehicle An emergency vehicle is a vehicle used by emergency services. Emergency vehicles typically have specialized emergency lighting and vehicle equipment that allow emergency services to reach calls for service in a timely manner, transport equipment ...
will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. Astronomer John Dobson explained the effect thus: In other words, if the siren approached the observer directly, the pitch would remain constant, at a higher than stationary pitch, until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial velocity does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity: v_\text = v_\text \cos(\theta) where \theta is the angle between the object's forward velocity and the line of sight from the object to the observer.


Astronomy

The Doppler effect for electromagnetic waves such as light is of widespread use in
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
to measure the speed at which
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s and galaxies are approaching or receding from us, resulting in so called
blueshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase i ...
or
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
, respectively. This may be used to detect if an apparently single star is, in reality, a close binary, to measure the rotational speed of stars and galaxies, or to detect exoplanets. This effect typically happens on a very small scale; there would not be a noticeable difference in visible light to the unaided eye. The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of discrete lines in the spectra of stars. Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s ( BD-15°4041, also known as LHS 52, 81.7 light-years away) and −260 km/s ( Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching. Redshift is also used to measure the expansion of space, but this is not truly a Doppler effect. Rather, redshifting due to the expansion of space is known as cosmological redshift, which can be derived purely from the Robertson-Walker metric under the formalism of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. Having said this, it also happens that there ''are'' detectable Doppler effects on cosmological scales, which, if incorrectly interpreted as cosmological in origin, lead to the observation of redshift-space distortions.


Radar

The Doppler effect is used in some types of
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor v ...
, to measure the velocity of detected objects. A radar beam is fired at a moving target — e.g. a motor car, as police use radar to detect speeding motorists — as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's velocity. Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc. Because the doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative velocity \Delta v is twice that from the same target emitting a wave: \Delta f=\fracf_0.


Medical

An echocardiogram can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the
ultrasound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies ...
beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the
cardiac output In cardiac physiology, cardiac output (CO), also known as heart output and often denoted by the symbols Q, \dot Q, or \dot Q_ , edited by Catherine E. Williamson, Phillip Bennett is the volumetric flow rate of the heart's pumping output: th ...
.
Contrast-enhanced ultrasound Contrast-enhanced ultrasound (CEUS) is the application of ultrasound contrast medium to traditional medical sonography. Ultrasound contrast agents rely on the different ways in which sound waves are reflected from interfaces between substances. T ...
using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements. Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (''when'' the received signal arrives). Velocity measurements of blood flow are also used in other fields of
medical ultrasonography Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, mus ...
, such as obstetric ultrasonography and
neurology Neurology (from el, νεῦρον (neûron), "string, nerve" and the suffix -logia, "study of") is the branch of medicine dealing with the diagnosis and treatment of all categories of conditions and disease involving the brain, the spinal ...
. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like
stenosis A stenosis (from Ancient Greek στενός, "narrow") is an abnormal narrowing in a blood vessel or other tubular organ or structure such as foramina and canals. It is also sometimes called a stricture (as in urethral stricture). ''Stricture'' ...
.


Flow measurement

Instruments such as the laser Doppler velocimeter (LDV), and acoustic Doppler velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency.


Velocity profile measurement

Developed originally for velocity measurements in medical applications (blood flow), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive.


Satellites


Satellite navigation

The Doppler shift can be exploited for
satellite navigation A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location ( longitude, latitude, and altitude/ elevation) to hig ...
such as in Transit and DORIS.


Satellite communication

Doppler also needs to be compensated in satellite communication. Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal. After realizing that the Doppler shift had not been considered before launch of the
Huygens probe ''Huygens'' ( ) was an atmospheric entry robotic space probe that landed successfully on Saturn's moon Titan in 2005. Built and operated by the European Space Agency (ESA), launched by NASA, it was part of the ''Cassini–Huygens'' mission an ...
of the 2005 Cassini–Huygens mission, the probe trajectory was altered to approach
Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...
in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift. (offline as of 2006-10-14, se
Internet Archive version
Doppler shift of the direct path can be estimated by the following formula: f_ = \frac\cos\phi \cos\theta where v_\text is the velocity of the mobile station, \lambda_ is the wavelength of the carrier, \phi is the elevation angle of the satellite and \theta is the driving direction with respect to the satellite. The additional Doppler shift due to the satellite moving can be described as: f_ = \frac where v_ is the relative speed of the satellite.


Audio

The Leslie speaker, most commonly associated with and predominantly used with the famous
Hammond organ The Hammond organ is an electric organ invented by Laurens Hammond and John M. Hanert and first manufactured in 1935. Multiple models have been produced, most of which use sliding drawbars to vary sounds. Until 1975, Hammond organs generated ...
, takes advantage of the Doppler effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note.


Vibration measurement

A
laser Doppler vibrometer A laser Doppler vibrometer (LDV) is a scientific instrument that is used to make non-contact vibration measurements of a surface. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are ext ...
(LDV) is a non-contact instrument for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.


Developmental biology

During the segmentation of
vertebrate Vertebrates () comprise all animal taxa within the subphylum Vertebrata () ( chordates with backbones), including all mammals, birds, reptiles, amphibians, and fish. Vertebrates represent the overwhelming majority of the phylum Chordata, with ...
embryo An embryo is an initial stage of development of a multicellular organism. In organisms that reproduce sexually, embryonic development is the part of the life cycle that begins just after fertilization of the female egg cell by the male spe ...
s, waves of
gene expression Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. T ...
sweep across the presomitic
mesoderm The mesoderm is the middle layer of the three germ layers that develops during gastrulation in the very early development of the embryo of most animals. The outer layer is the ectoderm, and the inner layer is the endoderm.Langman's Medical Emb ...
, the tissue from which the precursors of the
vertebra The spinal column, a defining synapomorphy shared by nearly all vertebrates, Hagfish are believed to have secondarily lost their spinal column is a moderately flexible series of vertebrae (singular vertebra), each constituting a characteristi ...
e ( somites) are formed. A new somite is formed upon arrival of a wave at the anterior end of the presomitic mesoderm. In zebrafish, it has been shown that the shortening of the presomitic mesoderm during segmentation leads to a Doppler-like effect as the anterior end of the tissue moves into the waves. This effect contributes to the period of segmentation.


Inverse Doppler effect

Since 1968 scientists such as Victor Veselago have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the refractive index of the medium a wave is traveling through. But some materials are capable of negative refraction, which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift. The first experiment that detected this effect was conducted by Nigel Seddon and Trevor Bearpark in
Bristol Bristol () is a City status in the United Kingdom, city, Ceremonial counties of England, ceremonial county and unitary authority in England. Situated on the River Avon, Bristol, River Avon, it is bordered by the ceremonial counties of Glouces ...
,
United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and ...
in 2003. Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a Vavilov–Cherenkov cone.


See also

* Bistatic Doppler shift * Differential Doppler effect * Doppler cooling *
Dopplergraph A dopplergraph or dopplergram is a two-dimensional representation of the approaching and receding motions of an object or area. The word "dopplergraph" is a combination of the words doppler and photograph. Dopplergraphs are two-dimensional records ...
*
Fading In wireless communications, fading is variation of the attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is ...
* Fizeau experiment * Photoacoustic Doppler effect * Range rate *
Rayleigh fading Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmissio ...
*
Redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
* Laser Doppler imaging * Relativistic Doppler effect


Primary sources


References


Further reading

* Doppler, C. (1842). '' Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (About the coloured light of the binary stars and some other stars of the heavens)''. Publisher: Abhandlungen der Königl. Böhm. Gesellschaft der Wissenschaften (V. Folge, Bd. 2, S. 465–482) roceedings of the Royal Bohemian Society of Sciences (Part V, Vol 2) Prague: 1842 (Reissued 1903). Some sources mention 1843 as year of publication because in that year the article was published in the Proceedings of the Bohemian Society of Sciences. Doppler himself referred to the publication as "Prag 1842 bei Borrosch und André", because in 1842 he had a preliminary edition printed that he distributed independently. * "Doppler and the Doppler effect", E. N. da C. Andrade, ''Endeavour'' Vol. XVIII No. 69, January 1959 (published by ICI London). Historical account of Doppler's original paper and subsequent developments. * David Nolte (2020). ''The fall and rise of the Doppler effect.'' Physics Today, v. 73, pgs. 31 - 35
DOI: 10.1063/PT.3.4429
*


External links

*

ScienceWorld {{DEFAULTSORT:Doppler Effect Wave mechanics Radio frequency propagation Radar signal processing Sound Acoustics